{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_style('darkgrid')\n",
    "plotBlue = sns.color_palette()[0]\n",
    "np.random.seed(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anomaly Detection & Probabilistic Programming\n",
    "\n",
    "This post will present a short survey on popular methods in anomaly detection. After exploring some of the goals and limitations of these methods, we will suggest that probabilistic programming provides an easy way to formulate more robust anomaly detection models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is Anomaly Detection?\n",
    "\n",
    "Anomaly detection algorithms detect observations that are significantly different from most of what you've seen before.\n",
    "\n",
    "One classic example here is in detecting credit card fraud: how do we automatically detect purchases that a legitimate credit card owner is very unlikely to have made?\n",
    "\n",
    "Another is in systems security: how do we detect activity on a network that's unlikely to be caused be a legitimate user?\n",
    "\n",
    "Anomaly detection is often done by building a probabilistic model of your data. This means you can see what the probability of observing every possible event is under your model. When you observe an event that has sufficiently low probability, you label it as anomalous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Challenges in Anomaly Detection\n",
    "\n",
    "In this post, we'll explore some of the standard techniques for building these probabilistic models from observed data, starting from the simplest and increasing in complexity. We’ll find that some of the traditional approaches involve manually manipulating distributions until they ‘look’ right. We’ll also find that appropriately expressing the relationships between features quickly becomes difficult and inexact. Lastly, the traditional methods make it difficult to propagate uncertainty through multiple steps of our algorithm.\n",
    "\n",
    "We'll conclude by looking at probabilistic programming languages that can help overcome each of those limitations with minimal friction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normally Distributed Single Variable\n",
    "\n",
    "In this section, we will see how anomaly detection can work for observations with a single feature.\n",
    "\n",
    "The simplest possible case for anomaly detection is observational data with a single, normally distributed feature. We'll generate 1000 such observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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lPj4el8tcN7E3o3GZ17L6T/s4665nx1/P0MMZQ12Dj227vuTm63pd1vqr/7SPcZnXXtLr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\nU5CLiIiY2P8PpOceb8tHj6MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbdda60b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "X1 = np.random.normal(4, 12, N)\n",
    "f, axes = plt.subplots(nrows=2, sharex=True)\n",
    "axes[0].set_xlim(-50, 50)\n",
    "axes[0].scatter(X1, np.zeros(N), marker='x', c=plotBlue)\n",
    "axes[1].hist(X1, bins=50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "To model this data as a normal distribution, we take the mean and the standard deviation from the sample we have."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample Mean: 4.20741199577\n",
      "Sample Standard Deviation: 12.1008227886\n"
     ]
    }
   ],
   "source": [
    "sample_mean = X1.mean()\n",
    "sample_sigma = X1.std()\n",
    "print('Sample Mean:', sample_mean)\n",
    "print('Sample Standard Deviation:', sample_sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our estimate for the distribution therefore looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vW3JlhTQOkZM/YGgT+SGLzYGyc+2IMxkwOdYodzmymjU1EsZgLY5WtcIlinKXQzQqDG0i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\naBPR/98oGAWjYIgAADY8wipXirGyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbafc5400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower Bound: -27.0127107989\n",
      "Upper Bound: 35.4275347904\n"
     ]
    }
   ],
   "source": [
    "base = np.linspace(-50, 50, 100)\n",
    "normal = sp.stats.norm.pdf(base, sample_mean, sample_sigma)\n",
    "lower_bound = sample_mean - (2.58 * sample_sigma)\n",
    "upper_bound = sample_mean + (2.58 * sample_sigma)\n",
    "anomalous = np.logical_or(base < [lower_bound]*100, base > [upper_bound]*100)\n",
    "\n",
    "plt.plot(base, normal)\n",
    "plt.fill_between(base, normal, where=anomalous, color=[1, 0, 0, 0.4])\n",
    "plt.xlim(-50, 50)\n",
    "plt.show()\n",
    "print('Lower Bound:', lower_bound)\n",
    "print('Upper Bound:', upper_bound)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now we just have to decide on some 'epsilon' value, which dictates our probability threshold for anomalous events.  If we set epsilon to .01, we're saying that any draw for which there's a probability of 1% or less that it given the above distribution should be marked as anomalous.  These values are the upper and lower bounds for what we consider 'normal', and are represented in the graphs above by the area shaded in red."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at two sample draws to see if they're anomalous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8k2MG7YPPyE8REz+PiQWfkXd91LnjUePm+Iycz8gBAOiSCHIAAAxGkAMAYDCC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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbafa7e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X1, np.zeros(N), marker='x', c=plotBlue)\n",
    "plt.xlim(-50, 50)\n",
    "plt.scatter(-29, 0, marker='x', color='red', s=150, linewidths=3)\n",
    "plt.scatter(17, 0, marker='x', color='green', s=150, linewidths=3)\n",
    "plt.axvline(lower_bound, ymin=.25, ymax=.75, color='red', linewidth=1)\n",
    "plt.axvline(upper_bound, ymin=.25, ymax=.75, color='red', linewidth=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the red draw exceeds the lower bound, and would therefore come up as anomalous, whereas the green draw falls within the normal range.\n",
    "\n",
    "Note that we’re losing some uncertainty by doing it this way.  We’re using the sample mean and standard deviation directly as estimates for the population mean and standard deviation, but of course there is some uncertainty in those estimates.  This model has no mechanism for preserving that uncertainty; we get the same probability estimate for any given event regardless of how certain we are about our estimates for those parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-normally distributed single variable\n",
    "\n",
    "In this section, we’ll look at a slightly more complicated case, in which we have observations with a single feature that are not normally distributed.  This will demonstrate two additional shortcomings of the standard approach to anomaly detection.  First, we’ll have to manually manipulate the data to ‘look’ normal.  Second, there is no simple way to encode pre-existing knowledge about the distributions into the model.\n",
    "\n",
    "Imagine that our observations can only take on positive values, which is a common restriction. For simplicity, let's use the same observations we used earlier, but we'll simply drop all negative observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NyIBefuO6cgr7pl0fvHJBa9ZtNJ4Kiw3xBYAUyyksUV7R2mnXxkb6jafBYsRnvgAAGCO+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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7face9647898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X2 = X1[X1 > 0]\n",
    "plt.hist(X2, bins=30)\n",
    "plt.xlim(-50, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just looking at the data, it seems that it no longer makes sense to model these observations as normally distributed.  Let's see what happens if we do try to model this as a normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XzkLjPwQemgGi43RLJpMhJmYaqqsv4+jRTNFxyImwnImoX9WU58NkbEaAje81t4qNnQYA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbaee8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lower Bound: -8.86419929781\n",
      "Upper Bound: 31.9838968773\n"
     ]
    }
   ],
   "source": [
    "sample_mean = X2.mean()\n",
    "sample_sigma = X2.std()\n",
    "base = np.linspace(-50, 50, 100)\n",
    "normal = sp.stats.norm.pdf(base, sample_mean, sample_sigma)\n",
    "lower_bound = sample_mean - (2.58 * sample_sigma)\n",
    "upper_bound = sample_mean + (2.58 * sample_sigma)\n",
    "anomalous = np.logical_or(base < [lower_bound]*100, base > [upper_bound]*100)\n",
    "\n",
    "plt.hist(X2, bins=30, normed=True, zorder=1)\n",
    "plt.fill_between(base, normal, where=anomalous, color=[1, 0, 0, 0.4], zorder=2)\n",
    "plt.plot(base, normal, color='black', zorder=3)\n",
    "plt.xlim(-50, 50)\n",
    "plt.show()\n",
    "print('Lower Bound:', lower_bound)\n",
    "print('Upper Bound:', upper_bound)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly this distribution does not fit our data!  Most obviously, it wouldn't declare an observation anomalous until it was less than ~ -8.9, while we already know that anything less than 0 is highly anomalous.  When we get into bayesian analysis and probabilistic programming we'll see how we can encode this prior knowledge into our models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the meanwhile, one common work around is to transform the observations until they look vaguely like they come from a normal distribution.  Common approaches for positive distributions include taking the logarithm of every observation, or raising it to a power less than 1.  With this data, it turns out that raising each observation to 0.55 produces something roughly normal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though this is common practice, especially in low-lift anomaly detection systems, eyeballing distribution transformations should make you suspicious.  It results in haphazard analysis and fuzzy statistical reasoning.  Again, probabilistic programming will give us the tools to make sure that all parameters we use in our model are calculated using legitimate statistical methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PHh3UhpqbgyvrSObxJFueR2trp+3ttbZ2WtreYLYFOIHVx8wX2Xl8RyInzMMJc5CCeyIx\n4MvRt27dUl5enjZs2KBFixZJkqZOnapz585Jkk6fPq2HHnooBFEBAIg9A+4JHzhwQLdv39a+fftU\nXl4ul8uloqIibd26VT09PcrMzNT8+fOHKisAAI4yYAkXFRWpqKjoa1+vqKgIWyAAAGIFJ+sAAMAQ\nTlsZoeycxN7uSe8BAGZQwhHKzknsW65fVtr4qWFMBQAIJUo4glk9iX13e1MY0wAAQo1jwgAAGEIJ\nAwBgCCUMAIAhlDAAAIbwxiwAjmBnWZ907wpxkkttbaMtnX/d652kuLg4y9sDvogSBuAIdpb1SfeW\n9o1KTlNCSnrQY7rbb2rPhoXKzJxsNSbwJZQwAMewuqxPure0z844IBQ4JgwAgCGUMAAAhlDCAAAY\nQgkDAGAIJQwAgCGUMAAAhlDCAAAYQgkDAGAIJQwAgCGUMAAAhlDCAAAYwrmjg9TX16erV69ausqK\nJFtXdQEAxAZKOEj19deUv/u4pSutSPeu0JI2fmqYUgEAohklbIHdK7QAAPBNOCYMAIAhQZVwbW2t\nVqxYIUm6fPmysrKytHLlSq1cuVLvvvtuWAMCAOBUAV+OPnTokI4dO6bExERJ0oULF7R69WqtWrUq\n3NkAAHC0gHvCGRkZKi8v7//84sWLOnXqlHJzc1VUVKTu7u6wBgQAwKkClnBOTo7i4uL6P58xY4Ze\neuklVVZWasKECdq7d29YAwIA4FSW3x2dnZ2t5ORkSfcKeuvWrUGN83iSrW4qorS1JZmOACCCpKYm\nRez/tUjNZYUT5hAMyyWcl5enzZs36/vf/75qamo0ffr0oMY1N3dYDhdJrJ6kA4CztbZ2RuT/NY8n\nOSJzWeGEOUjBPZGwXMIvv/yytmzZovj4eHk8HpWVldkKBwBArAuqhMeNG6cjR45IkqZNm6aqqqqw\nhgIAIBZwsg4AAAyJydNW9vX1qb7+mqUxXIgBABBqMVnCdi7GwIUYAAChFpMlLFm/GAMXYgAAhBrH\nhAEAMIQSBgDAEEoYAABDKGEAAAyhhAEAMIQSBgDAEEoYAABDKGEAAAyhhAEAMIQSBgDAEEoYAABD\nKGEAAAyhhAEAMIQSBgDAEEoYAABDKGEAAAyhhAEAMIQSBgDAEEoYAABDKGEAAAyhhAEAMIQSBgDA\nkKBKuLa2VitWrJAkNTQ0aPny5crNzVVpaWlYwwEA4GQBS/jQoUMqLi5WT0+PJGn79u1av369Kisr\n5fP5VF1dHfaQAAA4UcASzsjIUHl5ef/nFy9e1MyZMyVJWVlZqqmpCV86AAAcLGAJ5+TkKC4urv9z\nv9/f/3FiYqI6OjrCkwwAAIcbZnWA2/3f3u7q6tLo0aODGufxJFvdVNi0tSWZjgAgyqWmJkXU/7Uv\nitRcVjhhDsGwXMLTpk3TuXPn9PDDD+v06dOaNWtWUOOamyNnj7m1tdN0BABRrrW1M6L+r33O40mO\nyFxWOGEOUnBPJCyXcEFBgTZv3qyenh5lZmZq/vz5tsIBABDrgirhcePG6ciRI5Ikr9erioqKsIYC\nACAWcLIOAAAMoYQBADCEEgYAwBBKGAAAQyhhAAAMoYQBADCEEgYAwBBKGAAAQyyfMQsAYp3f51ND\nw8e2xnq9k750URzENkoYACz6tKNZr719SwkpNyyN626/qT0bFiozc3KYkiHaUMIAYENCSrqSxo4z\nHQNRjmPCAAAYQgkDAGAIJQwAgCGUMAAAhlDCAAAYQgkDAGAIJQwAgCGUMAAAhlDCAAAYQgkDAGAI\nJQwAgCFRfe7ovr4+1ddfszzO7tVPAAAIpagu4fr6a8rffVwJKemWxrVcv6y08VPDlAoAgOBEdQlL\n9q5k0t3eFKY0AAAEj2PCAAAYYntP+Mknn1RSUpIkafz48dq2bVvIQgEAEAtslfDdu3clSYcPHw5p\nGAAAYomtl6OvXLmi7u5u5eXladWqVaqtrQ11LgAAHM/WnvDIkSOVl5enpUuXqr6+Xs8++6xOnDgh\nt9v+Ieb/9161/n2jxdKYWzf/V1Kq7W0CAGCSrRL2er3KyMjo/3jMmDFqbm7Wd77znW8d4/EkD/gz\na///J/pX13hLOW63fKZB9D4ADLnU1KSA/w8HK9w/fyg4YQ7BsFXC77zzjq5evaqSkhI1NTWpq6tL\nHo9nwDHNzR0D3n7nTo+dKAAQVVpbOwP+PxwMjyc5rD9/KDhhDlJwTyRslfCSJUtUWFio5cuXy+12\na9u2bYN6KRoAgFhkq4Tj4+P16quvhjoLAAAxhd1XAAAMoYQBADAk6s8dDQDRwu/z2b6Km9c7SXFx\ncSFOBNMoYQAYIp92NOu1t28pIeWGpXHd7Te1Z8NCZWZODlMymEIJA8AQsnPlNzgXx4QBADCEEgYA\nwBBKGAAAQyhhAAAMoYQBADCEEgYAwBBKGAAAQyhhAAAMoYQBADCEEgYAwBBOWwkAEc7KhR/a2pLU\n2tqpvr4+SS7FxVnf1+JiEUOHEgaACGfnwg8t1y9rVHKaElLSLW2Li0UMLUoYAKKA1Qs/dLc3cbGI\nKMAxYQAADKGEAQAwhBIGAMAQShgAAEN4YxYAoJ+V5VBfZXVpU19fn+rrr33t658vsxponFOWX1HC\nAIB+dpZDSfaWNtXXX1P+7uOWl1E5afkVJQwA+JKhXNpkZ1tOWn7FMWEAAAyxtSfs9/v18ssv68MP\nP9Tw4cP1yiuvaMKECaHOBgCAo9naE66urtbdu3d15MgRvfjii9q+fXuocwEA4Hi2Svgf//iH5syZ\nI0maMWOGLly4ENJQAADEAlsvR3d2dio5Ofm/P2TYMPl8Prnd9g8x993pkO8/560Nar+pbneq5W19\n2tEqyRX2MUM9joyhGUdGs+PIGJpxQ52xu/2m5aVNDQ0fq7v9puVtDSZjpLFVwklJSerq6ur/PJgC\n9niSB7z94Bub7UQBAESpWbN+oKeeWmQ6hlG2dl1/8IMf6P3335ckffDBB5oyZUpIQwEAEAtcfr/f\nb3XQF98dLUnbt2/XxIkTQx4OAAAns1XCAABg8DhZBwAAhlDCAAAYQgkDAGAIJQwAgCFhvYqSk84x\nXVtbq1dffVUVFRWmo9jS29urTZs2qbGxUT09PVqzZo0ee+wx07Es8/l8Ki4uVl1dndxut0pLS3X/\n/febjmVLS0uLFi9erLfeeitqVxc8+eSTSkpKkiSNHz9e27ZtM5zInoMHD+rkyZPq6enR8uXLtXjx\nYtORLPnTn/6ko0ePyuVy6c6dO7py5YrOnDnT/7uJFr29vSooKFBjY6OGDRumLVu2RN1j4+7duyos\nLNT169eVlJSkkpISffe73/3W7w9rCX/xHNO1tbXavn279u3bF85NhsWhQ4d07NgxJSYmmo5i2/Hj\nxzV27Fjt2rVL7e3teuKJJ6KyhE+ePCmXy6WqqiqdPXtWr7/+elT+TfX29qqkpEQjR440HcW2u3fv\nSpIOHz5sOMngnD17Vv/85z915MgRdXd363e/+53pSJYtWrRIixbdO+lFWVmZlixZEnUFLEnvv/++\nfD6fjhw5or/97W/69a9/rTfffNN0LEv++Mc/KjExUW+//bbq6upUWlqq3/72t9/6/WF9Odop55jO\nyMhQeXm56RiDsmDBAuXn50u6tzc5bFh0Xko6OztbW7ZskSQ1NjYqJSXFcCJ7du7cqWXLlik93dpF\nySPJlStX1N3drby8PK1atUq1tbWmI9ny17/+VVOmTNHPf/5zrV27Vo8++qjpSLadP39eH330kZYu\nXWo6ii1er1d9fX3y+/3q6OhQfHy86UiWffTRR8rKypIkTZw4UdeuXRvw+8P6nzgc55g2IScnR42N\njaZjDMqoUaMk3fud5Ofn64UXXjCcyD63262NGzequro66p4lS9LRo0eVlpam2bNna//+/abj2DZy\n5Ejl5eVp6dKlqq+v17PPPqsTJ05E3eO7ra1Nn3zyiQ4cOKB///vfWrt2rd577z3TsWw5ePCg1q1b\nZzqGbYmJibp+/brmz5+v//znPzpw4IDpSJZNnTpVp06dUnZ2tj744APdvHlTfr9fLtc3n+s6rI8W\nO+eYRvjcuHFDzzzzjBYtWqQf//jHpuMMyo4dO3TixAkVFxfrs88+Mx3HkqNHj+rMmTNasWKFrly5\nooKCArW0tJiOZZnX69XChQv7Px4zZoyam5sNp7JuzJgxmjNnjoYNG6aJEydqxIgRam1tNR3Lso6O\nDtXX1+uRRx4xHcW23//+95ozZ45OnDih48ePq6CgoP+wR7RYvHixEhMT9fTTT+vPf/6zpk+f/q0F\nLIW5hJ12juloPrnYrVu3lJeXpw0bNvQfO4pGx44d08GDByVJI0aMkNvtjrondpWVlaqoqFBFRYUe\neOAB7dy5U2lpaaZjWfbOO+9ox44dkqSmpiZ1dXXJ4/EYTmXdQw89pL/85S+S7s3js88+09ixYw2n\nsu7cuXOaNWuW6RiDkpKS0n8sOzk5Wb29vfL5fIZTWXP+/Hn98Ic/1B/+8Af96Ec/Cvhm5LC+HJ2T\nk6MzZ87oZz/7maR755iOZgM9m4l0Bw4c0O3bt7Vv3z6Vl5fL5XLp0KFDGj58uOlolsybN0+FhYXK\nzc1Vb2+vioqKom4OXxTNf1NLlixRYWGhli9fLrfbrW3btkXdEyJJmjt3rv7+979ryZIl8vv9Kikp\nicrfS11dXdSuPvncM888o02bNunpp59Wb2+vXnzxxah782JGRob27Nmj/fv3a/To0XrllVcG/H7O\nHQ0AgCHR97QVAACHoIQBADCEEgYAwBBKGAAAQyhhAAAMoYQBADCEEgYAwJD/A+TEjPpPHNKDAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbae50d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X3 = X2 ** 0.55\n",
    "plt.hist(X3, bins=30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We won't go through it here, but the next steps would be to run the same kind of analysis we ran on the data that actually was normally distributed, and to then check whether a new observation to the power 0.55 seemed anomalous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple Independently Distributed Normal Variables\n",
    "\n",
    "So far we've only been looking at observations with a single feature. We'll now expand our analysis to multiple variables. Initially we will assume that they are independently normal distributed. That is, that each feature is normally distributed, and there is no correlation between them.  Though this is still a simple example, this simple multi-dimensional case will set the stage for evaluating how the traditional methods of anomaly detection perform on more realistic data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NJ3DJ30wsBEggz0P8N+Q0lRuM/SpYdmPQTddmB5jpIqkMA7jcPq15MMxGHekB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbacf14e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "X1 = np.random.normal(4, 12, N)\n",
    "X2 = np.random.normal(9, 5, N)\n",
    "plt.scatter(X1, X2, c=plotBlue)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we can estimate the means and standard deviations of the normal distributions through the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample Mean 1: 3.07957128984\n",
      "Sample Mean 2: 9.02005010207\n",
      "Sample Standard Deviation 1: 12.1382458997\n",
      "Sample Standard Deviation 2: 4.76924679208\n"
     ]
    }
   ],
   "source": [
    "x1_sample_mean = X1.mean()\n",
    "x2_sample_mean = X2.mean()\n",
    "x1_sample_sigma = X1.std()\n",
    "x2_sample_sigma = X2.std()\n",
    "print('Sample Mean 1:', x1_sample_mean)\n",
    "print('Sample Mean 2:', x2_sample_mean)\n",
    "print('Sample Standard Deviation 1:', x1_sample_sigma)\n",
    "print('Sample Standard Deviation 2:', x2_sample_sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we would expect, these are not far from the actual values we used to generate the data.\n",
    "\n",
    "Next, let's look at a heatmap of where we would expect to find observations given the joint probability distributions implied by these distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i0GG43R7kDRmBr91hvNa2PDfcFPTBnzsMg752O4oBHNz2HtLsudj+2RfIGzgE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\nMJCJiIgEwEAmIiISwP8HTE6VKUnkm4oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbad43940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta = 0.025\n",
    "x1 = np.arange(-40, 50, delta)\n",
    "x2 = np.arange(-40, 50, delta)\n",
    "x, y = np.meshgrid(x1, x2)\n",
    "z = plt.mlab.bivariate_normal(x, y, x1_sample_sigma, x2_sample_sigma, x1_sample_mean, x2_sample_mean)\n",
    "plt.contourf(x, y, z, cmap='Blues_r')\n",
    "thinned_points = np.array([n in np.random.choice(N, 300) for n in range(N)])\n",
    "plt.scatter(X1[thinned_points], X2[thinned_points], c='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the two variables are independent, we get this nice concentric circle shape, where as we move in towards the means, we're increasingly likely to draw an observation with those features. As we move away, we're less likely to see an observation with features at those values. We might, for instance, decide that anything in the dark-blue region is anomalous.\n",
    "\n",
    "Note that because the distribution of the vertical feature has a smaller variance, the area of high probability is much thinner vertically than it is horizontally."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple Jointly Distributed Features\n",
    "\n",
    "In this section, we’ll look at some slightly more realistic data.  We will try to use some of the methods we’ve built up to this point to tackle this more complex data.  \n",
    "\n",
    "To build up more of an intuition of what’s going on, let's say that we're observing database transactions, and for each observation we record the latency and the average number of concurrent connections over the course of the transaction.\n",
    "\n",
    "We expect these to be positively correlated - the database takes longer to process any given query as the number of active connections grows.  \n",
    "\n",
    "We also know that neither of these features can be negative - you cannot have fewer than zero connections to the database, and you cannot finish a transaction before you start it (negative latency)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rcCGBIrJKruIPA54g1m7ZndaEm6lFwU3bWrGrrZd97QtGYNDrko4jW/dI7rqy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\niiAIgrAkJFAEQRCEJfn/QrAWQp2++N8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbac832b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def positive_support_normal(mean, sigma, n):\n",
    "    xs = np.random.normal(mean, sigma, n)\n",
    "    for i, num in enumerate(xs):\n",
    "        while num < 0:\n",
    "            num = np.random.normal(mean[i], sigma)\n",
    "        xs[i] = num\n",
    "    return xs\n",
    "    \n",
    "N = 1000\n",
    "\n",
    "mu_cons = 10\n",
    "sigma_cons = 6\n",
    "sigma_latency = 20\n",
    "beta = 3\n",
    "\n",
    "cons = positive_support_normal(np.array([mu_cons]*N), sigma_cons, N)\n",
    "latency = positive_support_normal(beta * cons, sigma_latency, N)\n",
    "ax = sns.jointplot('cons', 'latency', pd.DataFrame({'cons': cons, 'latency': latency}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now if we use our previous method - where we treat each feature as independently normally distributed - to think about the probability of finding observations with a particular combination of features, we'll see something like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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h8/lgtVox4Ds5qcQ8TqQ9Hg9aWlpQ4mnCSYcy4vzUJY5INgmJeUNDA2pqamZ6LcQZzGyK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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbac4fa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta = 0.025\n",
    "x1 = np.arange(-5, 35, delta)\n",
    "x2 = np.arange(-20, 140, delta)\n",
    "x, y = np.meshgrid(x1, x2)\n",
    "z = plt.mlab.bivariate_normal(x, y, cons.std(), latency.std(), cons.mean(), latency.mean())\n",
    "plt.contourf(x, y, z, cmap='Blues_r')\n",
    "plt.scatter(cons, latency, c='gray')\n",
    "plt.ylabel('Latency')\n",
    "plt.xlabel('Connections')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem is that we're missing something about the relationship between the two features.  We _know_ that latency depends on the number of concurrent connections, but it's difficult to account for that in our model.\n",
    "\n",
    "There are a few ways to address this issue.  For example, we could engineer a new feature from the existing data that might capture some of the correlation between the two, and treat that as independently normally distributed as well. Alternatively, we could use the observed data to estimate the covariance relation between the two features and keep trying to model them as a multivariate normal distribution.\n",
    "\n",
    "Any of these steps quickly get complicated and, more importantly, imprecise.  So far we've only explored relatively simple distributions with very small numbers of features.  Each feature needs to be  be transformed somehow to the normal.  We might need to build new features by hand to improve our models properties, and most often we'll assume that if features are correlated, they at least have joint normal distributions.\n",
    "\n",
    "Assumptions about distributions are a good place to start, but we should be able to learn from the data in a more robust and systematic way than eyeballing the value of added features or distribution transformations.\n",
    "\n",
    "That's exactly where Bayesian modeling and probabilistic programming come in."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian modeling \n",
    "\n",
    "Bayesian modeling is a way of calculating the likelihood of some observation, given the data you've already seen.  It allows you to declare your statistical beliefs about what your data _should_ look like before you look at the data.  These beliefs are known as 'priors'.  You can declare one for each of the parameters you're interested in estimating. Bayesian modeling looks at these priors and the observed data, and calculates a distribution for each of those parameters.  These are known as 'posterior distributions'.  \n",
    "\n",
    "Part of the benefit of probabilistic programming, relative to comparable Bayesian modeling in the past, is that you don't need to know anything about how that calculation happens.\n",
    "\n",
    "### Probabilistic Programming\n",
    "\n",
    "Roughly speaking, the steps involved in probabilistic programming are as follows:\n",
    "\n",
    "1. Declare your prior beliefs about what the data looks like.\n",
    "2. Feed in your data.\n",
    "3. A sampling algorithm will return a posterior distribution for each of the parameters in your model.\n",
    "\n",
    "Probabilistic programming languages enable you to state your priors beliefs and your model with elegant, statistical syntax.  \n",
    "\n",
    "The more data you have to learn from, the less your prior beliefs matter, and generally the tighter the distributions you'll get for your model parameters.\n",
    "\n",
    "There are several advantages here.  First, you get a formal way to encode your knowledge about the data into your model.  As we saw earlier, this is especially useful when you know that there is no chance at all of certain observations.\n",
    "\n",
    "Second, there are no limitations on which distributions we can use to model our world, or on the hierarchical relations we claim they have.  Which  means, among other things, that and we don't have to estimate data manipulations to make things look right.\n",
    "\n",
    "Third, we get to propagate our uncertainty.  For example, instead of simply estimating the mean of the population distribution as the sample mean, we estimate the population mean as a distribution itself, and the nature of this uncertainty will affect our final model of the data.\n",
    "\n",
    "It's simpler than ever to build a complex model of the world."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Simple Example\n",
    "\n",
    "The example below is constructed using the python interface to [Stan](http://mc-stan.org/), which is one of the most mature probabilistic programming language out there today.  \n",
    "\n",
    "Stan is a compiled language.  In the code below, we store the Stan model as a python string.  The Stan model is then compiled and passed the data we define in the `data` named parameter to the `pystan.stan` function.\n",
    "\n",
    "Here we can finally overcome a few of the difficulties we encountered earlier.  First, we can declare that neither variable can take on a negative value.  Second, we can create a simple hierarchical model that encodes our beliefs about the data.  In this case, we expect latency to depend on the number of concurrent connections, and we can declare that.  Finally, we can propagate our uncertainty throughout the model.\n",
    "\n",
    "This is not a Stan tutorial, so we won't go into great detail on how to do this, but the Stan code below is commented so as to provide an intuition for how it all works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left column of graphs represent the posterior distributions of parameters.\n",
      "The right column of graphs plot the samples drawn from those distributions.\n"
     ]
    },
    {
     "data": {
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Vq1asX78eKO+WV+o2JFK/WCwCK3ecocRoZtYDUfh7N7197gHdWvDjwST2H09l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\n9Wq35QUAWJbFmjVrkJ6ejqlTp3okL202MjIykJKSgvj4eLfm48iRI1CpV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7face96476d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pystan\n",
    "\n",
    "model_code = \"\"\"\n",
    "    data {\n",
    "        int<lower=0> N;             // number of observations\n",
    "        vector<lower=0>[N] latency; // observed latency\n",
    "        vector<lower=0>[N] cons;    // observed concurrent connections\n",
    "        \n",
    "        real latency_test;          // test for event probabilities\n",
    "        real cons_test;             // test for event probabilities\n",
    "    }\n",
    "\n",
    "    parameters {\n",
    "        real mu_cons;               // mean of concurrent connections\n",
    "        real sigma_cons;            // sigma of concurrent connections\n",
    "        real sigma_latency;         // sigma of latencies\n",
    "        real beta;                  // linear coefficient for connections in latency\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        // declare some weak prior beliefs about our parameters\n",
    "        mu_cons ~ normal(100, 100);\n",
    "        sigma_cons ~ normal(100, 100);\n",
    "        sigma_latency ~ normal(100, 100);\n",
    "        beta ~ uniform(-100, 100);\n",
    "    \n",
    "        // both these distributions are truncated below at 0.0\n",
    "        for (i in 1:N) {\n",
    "            cons[i] ~ normal(mu_cons, sigma_cons) T[0.0,];\n",
    "            \n",
    "            // latency is linearly related to cons \n",
    "            latency[i] ~ normal(beta * cons[i], sigma_latency) T[0.0,];\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    generated quantities {\n",
    "        real prob_cons;\n",
    "        real prob_latency;\n",
    "        real prob;\n",
    "\n",
    "        prob_cons <- 2 * (.5 - abs(.5 - normal_cdf(cons_test, mu_cons, sigma_cons)));\n",
    "        prob_latency <- 2 * (.5 - abs(.5 - normal_cdf(latency_test, beta * cons_test, sigma_latency)));\n",
    "        prob <- prob_cons * prob_latency;\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'latency': latency,\n",
    "    'cons': cons,\n",
    "    'latency_test': 3.,\n",
    "    'cons_test': 3.,\n",
    "}\n",
    "\n",
    "fit = pystan.stan(model_code=model_code, data=data)\n",
    "fit.plot(['mu_cons', 'sigma_cons', 'beta', 'sigma_latency'])\n",
    "print('The left column of graphs represent the posterior distributions of parameters.')\n",
    "print('The right column of graphs plot the samples drawn from those distributions.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stan will also provide summary statistics about each parameter in the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_39252ec70065ee074bb53919d98789f1.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "                mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "mu_cons        10.02  7.2e-3   0.23   9.56   9.87  10.02  10.17  10.46    987    1.0\n",
      "sigma_cons      5.88  5.7e-3   0.18   5.54   5.75   5.87   5.99   6.24   1006    1.0\n",
      "sigma_latency  20.81    0.02   0.58  19.73  20.42  20.79  21.19  21.99   1073    1.0\n",
      "beta            2.91  1.9e-3   0.06   2.78   2.87   2.91   2.95   3.03   1048    1.0\n",
      "prob_cons       0.23  8.2e-4   0.02   0.19   0.22   0.23   0.25   0.29    907    1.0\n",
      "prob_latency    0.78  3.3e-4   0.01   0.76   0.78   0.78   0.79    0.8    970    1.0\n",
      "prob            0.18  6.5e-4   0.02   0.15   0.17   0.18   0.19   0.22    899    1.0\n",
      "lp__           -5451    0.05   1.45  -5455  -5452  -5451  -5450  -5449    791    1.0\n",
      "\n",
      "Samples were drawn using NUTS(diag_e) at Wed May  4 12:05:52 2016.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly, Stan effectively recovers the parameters we used to generate the data.  As you can see, the output is not simply a point estimate for each parameter.  The fit object stores a distribution for each of the parameters, so that your uncertainty about them can be propagated through to the end.\n",
    "\n",
    "In this case we’re checking whether an observation with 3 concurrent connections and a latency measure of 3 is anomalous.  The model returns ~20% probability of seeing a more extreme value, so we conclude that it is not anomalous.  We can see that we even get a distribution over the probability of seeing the event in question, not just a point estimate.  This can be invaluable in anomaly detection.\n",
    "\n",
    "For the sake of comparison, let's graph a contour plot similar to the one above.  In this case we'll simply calculate point estimates of the probability at each x,y coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oSdv7zc9fytdeP9KNuDBVUkjDxE2oP7NDwdYBCftHJGwdkLhuPQ++X/XN1W/T5/MhGo1m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\nxzHMiYiIPO7/Bx7cXaAji292AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facb6470cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary = fit.summary()\n",
    "means = dict(zip(summary['summary_rownames'], [s[0] for s in summary['summary']]))\n",
    "\n",
    "delta = .1\n",
    "x1 = np.arange(-5, 35, delta)\n",
    "x2 = np.arange(-20, 140, delta)\n",
    "x, y = np.meshgrid(x1, x2)\n",
    "\n",
    "z = np.zeros((x.shape[0], y.shape[1]))\n",
    "\n",
    "def extreme(val, mu, sig):\n",
    "    return 2 * (.5 - abs(.5 - sp.stats.norm.cdf(val, mu, sig)))\n",
    "\n",
    "for i, con in enumerate(x[0]):\n",
    "    for j, lat in enumerate(y[:,0]):\n",
    "        con_prob = extreme(con, means['mu_cons'], means['sigma_cons']) \n",
    "        lat_prob = extreme(lat, means['beta'] * con, means['sigma_latency'])\n",
    "        z[j, i] = con_prob * lat_prob if con >= 0 and lat >= 0 else 0\n",
    "\n",
    "plt.contourf(x, y, z, cmap='Blues_r')\n",
    "thinned_points = np.array([n in np.random.choice(N, 500) for n in range(N)])\n",
    "plt.scatter(cons[thinned_points], latency[thinned_points], color='gray')\n",
    "plt.ylabel('Latency')\n",
    "plt.xlabel('Connections')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that our model of the probability of a particular observation captures the relationship between features in our data."
   ]
  },
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    "### Conclusion\n",
    "\n",
    "In the probabilistic programming code above, we do some relatively advanced modeling.  We are able to declare our prior beliefs about the distributions model, truncate distributions at arbitrary points, and treat our observed features hierarchically.  Stan takes our declarations, which are written in simple, statistical syntax, and runs a sampling algorithm to find the posterior distributions of our models.  Using these posterior distributions, we can evaluate the likelihood of an observation given our data (and our priors).  \n",
    "\n",
    "Hopefully this hints at how probabilistic programming allows for a simple way to create easily customizable models for use in anomaly detection.  Powerful anomaly detection, though, is only the beginning of what you can do with probabilistic programming."
   ]
  }
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